Hilda Mason, the City Council's unquestioned champion of the public schools, looked frustrated and bitter last week as she played out a losing hand in trying to scrape together an additional $4 million for next year's school budget.

Some of her colleagues say privately that Mason (Statehood-At Large) did neither the schools nor herself a favor by stubbornly trying to tack on the extra funds to the 1984 school budget.

But more importantly, Mason's doomed-from-the-start posturing symbolized the stunning reversal of the public schools' political fortunes.

A year ago, Mason, chairman of the Education Committee, and other school board allies easily won approval of an amendment to the 1983 budget that added $16 million to the amount proposed by Mayor Marion Barry.

Their success was aided in part by the cheerleading of then-council chairman Arrington Dixon, who played on the reluctance of Barry and council members to appear anti-education in an election year.

They also were aided by the council budget process that year, which gave committee chairmen like Mason more influence in shaping the budget before the full council voted on it.

This year, it was a different story.

Barry, reelected last fall to his second four-year term, was willing to take on the schools this time around. David A. Clarke, the former Ward 1 council member who replaced Dixon as chairman, has always wanted closer scrutiny of school spending, especially now with declining enrollments and tight economic times.

The change in the council's budget process, instituted by Clarke, was a decisive factor in neutralizing what little influence Mason had this year.

In the past, committee chairmen promoting pet budget issues could lock in committee votes that were difficult to turn around on the floor of the council.

This year, committee chairmen were limited to making non-binding recommendations to Clarke, who then prepared an overall response to Barry's budget recommendations.

Also, a lot of disagreements that Dixon previously thrashed out on the floor were worked out quietly, behind the scenes, by Clarke. A few council members griped that Clarke's quiet diplomacy bordered on back-room dealing. But most members complimented Clarke for providing what they said was long-overdue leadership.

The revamped budget process this year left little, if any, room for the school board to drive a wedge, as it has in years past. The board's public relations offensive, warning of possible teacher layoffs and shortages of books and other supplies, didn't work.

The mayor proposed a 1984 operating budget for the schools totaling $318.5 million, an increase of $12 million over the current year, but $18 million less than the schools requested.

Mason sided with the school board, recommending the council make up most of the difference by raising income taxes. That proposal was never seriously considered, council members said.

Meanwhile, Clarke was negotiating with Barry and David H. Eaton, president of the school board. Eaton at one time said the board would settle for nothing less than $330 million, but privately, he set $328 million as the board's bottom line.

Clarke at one point offered to support $328 million if the board agreed to acknowlege that that amount constituted "full funding" for education, and if it would consider closing or clustering some schools to save money and avoid layoffs.

Negotiations collapsed when Eaton said he lacked the authority to accept the offer on behalf of the board.

Clarke then got Barry and a majority of the council to agree to $326 million.

Clarke also called on City Auditor Otis Troupe to do a quick analysis of the board's proposed budget. Troupe concluded the schools only needed $321 million to maintain services and staff. School officials dismissed the audit as a publicity stunt even while crediting Clarke with a clever maneuver.

In effect, the final vote was a formality, but Mason pressed on, convinced the school board was being treated shabbily and miffed by Clarke's successful maneuvering behind closed doors.

On the council floor, several of her colleagues cringed when she offered vague proposals for raising income taxes to pay for her plan, and urged her to give up. They said the schools could always come back later to ask for more money if they truly needed it.

Mason disagreed, demanded a vote and was decisively defeated.

At week's end, Mason defended her efforts, saying that the new budget might avert layoffs, but it provides no money to repair dilapidated schools or guarantee adequate supplies for students.

"They (other council members) don't look at the whole education environment, and that's why people are putting their kids in private schools," said Mason, a 66-year-old former teacher and school board member whose grandmotherly demeanor fades when she defends the schools.

As for Clarke's leading role in shaping the final version of the budget, Mason said: "That's too much power under one person. . . . I preferred and still prefer the way we did it in the past."

However, some of her colleagues think Mason was too shrill and obstinate in her public defense of the schools, long after the issue had been decided. They said such behavior undercuts her credibility on the Education Committee.

Although her aides insist they ask tough questions of the school board and superintendent, some council members said Mason perceives her role as school booster rather than watchdog.

As one of Mason's colleagues put it, "Hilda should have cooled it. . . . All of us want to protect things we feel strongly about . . . but what you need is some balance.